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# Essential mathematics 2

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Essential mathematics 2 (MST125) builds on the concepts and techniques in Essential mathematics 1 (MST124) to provide a complete foundation for higher-level mathematics studies. You’ll be introduced to a broad range of enjoyable and essential topics, such as proof, differential equations, mechanics and discrete mathematics, as well as extending your knowledge of calculus and its applications. You’ll use mathematical software, and learn how to typeset mathematics. To study this module you should have a sound knowledge of relevant mathematics as provided by Essential mathematics 1 (MST124), in particular basic calculus.

## What you will study

There are twelve study units in this module.

In the first unit, you’ll revise and consolidate the mathematics taught in Essential mathematics 1 (MST124).

In the remaining study units you’ll cover the following topics.

• Number theory: you’ll learn about divisibility properties of the integers. These have many practical applications, such as in cryptography.
• Conics: these are the curves obtained by slicing a cone along a plane. Their applications include modelling the motion of planets and other heavenly bodies.
• Geometric transformations: these include reflections, rotations and translations, and other similar ways of transforming geometric figures. You’ll use an algebraic approach, involving matrices and vectors.
• Mathematical language and proof: you’ll look at how mathematical results can be stated clearly, and how they can be proved to be true.
• Further calculus: you’ll extend your knowledge and skills in calculus.
• Differential equations: these are equations that involve an unknown function and one or more of its derivatives. They are used extensively in applied mathematics to model a range of situations involving quantities that change.
• Mechanics: you’ll analyse forces that act on stationary objects, and the motion of moving objects.
• Eigenvalues and eigenvectors: these are numbers and vectors associated with matrices, which arise in a range of situations in both pure and applied mathematics.
• Combinatorics: you’ll learn how to solve problems involving the positive integers, such as how many different ways there are to choose objects from a set. You’ll also study some interesting sequences of numbers, such as the Fibonacci sequence.

With a choice of three options of typesetting software, you’ll learn how to typeset mathematics.

You’ll work mainly from the module books, which are available in electronic formats as well as in print. You can view some of the worked examples in the books in an alternative video format, in which tutors work through and discuss the examples. You’ll use specially designed software applications to help you understand the concepts taught, and the same mathematics computer package as used in Essential mathematics 1 (MST124). There are many online interactive practice questions to help you consolidate your learning.

Read the full content list here.

### You will learn

In Essential mathematics 2 (MST125), you’ll further develop your mathematical skills and begin to develop new ones:

• thinking logically about mathematical problems
• expressing problems in mathematical language
• using mathematical techniques to find solutions to problems
• communicating mathematical ideas clearly and succinctly

### Professional recognition

This module can help you to gain membership of the Institute of Mathematics and its Applications (IMA).

## Entry requirements

You must have passed, or currently be studying, one of the following modules:

Or be able to provide evidence you have the required mathematical skills.

## Preparatory work

You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.

The key topics to revise include:

• algebraic manipulation and solving equations
• geometry and trigonometry
• exponentials and logarithms.

Essential mathematics 1 (MST124) is ideal preparation.

## You will need

We recommend a basic scientific Casio ‘Natural’ calculator such as the fx-83GTX PLUS or fx-85GTX PLUS. The module website includes a calculator guide with references to this series of calculator.

Note that the only type of calculator permitted in the final examination is a scientific calculator that does not offer algebraic manipulation, differentiation or integration, language translation or communication with other devices or with the internet. It should also not be programmable, and not have any retrievable information (such as databanks, dictionaries, mathematical formulas or text) stored in it.

### Computing requirements

You'll need a desktop or laptop computer with an up-to-date version of 64-bit Windows 10 (note that Windows 7 is no longer supported) or macOS and broadband internet access.

To join in spoken conversations in tutorials we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards and any modern browser is suitable for most activities.

Our OU Study mobile App will operate on all current, supported, versions of Android and iOS. It's not available on Kindle.

It's also possible to access some module materials on a mobile phone, tablet device or Chromebook, however, as you may be asked to install additional software or use certain applications, you'll also require a desktop or laptop as described above.

## Teaching and assessment

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.
• Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part.

### Assessment

The assessment details for this module can be found in the facts box above.

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

## If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying MST125 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

## Future availability

Essential mathematics 2 (MST125) starts twice a year – in February and October.

This page describes the module that will start in October 2021 and February 2022.

We expect it to start for the last time in October 2025.

### Course work includes:

3 Tutor-marked assignments (TMAs)
4 Interactive computer-marked assignments (iCMAs)
Examination
No residential school

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